System, apparatus, and method for measuring an oxygen concentration of a gas

ABSTRACT

An apparatus, system and method maximizes efficiency and accuracy of measuring an oxygen concentration of a measured gas by varying a flow of oxygen ions within a measuring cell ( 202 ) in accordance with an output signal of an oxygen sensor cell ( 206 ). The pump current ( 208 ) through a pump cell ( 204 ) is switched between a constant positive current and a constant negative current when upper and lower thresholds of the output signal are reached. The pulse width ratio of the square wave produced by the varying current is compared to a pulse width ratio function derived from a calibration procedure to determine the oxygen concentration of the measured gas.

RELATED APPLICATIONS

This application is a divisional patent application of U.S. patentapplication Ser. No. 10/699,182, filed on Nov. 01, 2003, now U.S. Pat.No. 6,978,655, entitled “System, Apparatus, And Method For Measuring AnOxygen Concentration Of A Gas” which claims the benefit of priority ofU.S. Provisional Application Ser. No. 60/443,628 filed on Jan. 30, 2003,entitled “System, Apparatus, And Method For Measuring An OxygenConcentration Of A Gas”, both hereby incorporated by reference in theirentirety herein.

BACKGROUND OF THE INVENTION

The invention relates in general to oxygen sensors and more specificallyto an apparatus, system and method for monitoring an oxygenconcentration of a gas.

Oxygen sensors are used to measure the concentration of oxygen in ameasured gas. Many conventional combustion engines utilize oxygensensors for determining the air to fuel mixture of the exhaust of thecombustion engine. Conventional internal combustion engines typicallyincorporate electronic fueling control using computing devices, such asElectronic Control Units (ECU), that meter fuel into the engine intakedepending on engine intake airflow. Typically, the volume of fuel isregulated such that emissions are minimized and all of the fuel iscompletely burned. The theoretical ratio of air to fuel for completecombustion is 14.7 by weight for gasoline, called the stoichiometricratio. Theoretically, all available fuel combines with all the intakeair at the stoichiometric ratio. The unit Lambda (λ) is often used torepresent the quotient of actual air to fuel ratio over the region nearthe stoichiometric ratio. Conventional electronic fueling systemstypically include an oxygen sensor in the exhaust that measures theoxygen concentration of the exhaust. These oxygen sensors act as fuelcells that create an output voltage by combining unburned hydrocarbonsin the exhaust with atmospheric oxygen. This results in a lambda/outputtransfer curve where a λ of 1.0 corresponds to an output voltage of0.45V. Using the oxygen sensor, the fueling control system regulates thefueling such that the resulting lambda is 1.0 at medium load conditionsusing a feedback loop. The transfer curve of a typical oxygen sensor isvery steep where λ is equal to 1.0, however, and significant variationsin output voltage occurs for slight variations in λ. Accordingly, themeasured voltage cannot be used to measure other λ values. At high loadconditions, a typical internal combustion engine produces maximum powerat lambda values <one (0.75 to 0.85). Conventional ECU systems operatein an ‘open loop’ mode under these conditions where the volume ofinjected fuel is derived solely from pre-stored maps that relate intakeair mass to fuel mass without feedback. Because engine aging andproduction variations change the actual air fuel ratio of the engine,these pre-stored conditions are not always correct for the particularengine. As a result, conventional systems are limited in that severeinefficiencies can occur at high load conditions.

Some recent developments in engine technology have resulted in‘lean-burn’ systems that operate at lambda ratios greater than 1 (up to1.1) to minimize fuel consumption and further minimize emissions usingspecial catalysators. Because ordinary lambda sensors are not usable inthese lambda regimens, a ‘wide-band’ or Universal Exhaust Gas Oxygen(UEGO) sensor has been developed. UEGO sensors combine a smallmeasurement chamber having an orifice open to the exhaust stream, astandard oxygen sensor (Nernst cell), and a pump cell. The pump cell isa solid-state device of porous ceramic that allows oxygen to movebetween the atmosphere and the measurement chamber. The direction andmagnitude of the current through the pump cell (often referred to as thepump current) determines the direction and flow rate of oxygen ions. Inconventional systems, an active feedback loop is incorporated such thatthe voltage at the oxygen sensor portion of the device is held at thestoichiometric voltage. The pump current can then be used to determinethe λ value over a wide range of ratios up to the ratio for free air.

FIG. 1 is graphical illustration of a typical relationship between thepump current and Lambda (λ). As shown in FIG. 1, the resulting curve ofpump current vs. lambda value (λ) is non-linear. Although the curveshape does not vary, manufacturing tolerances in the sensors result indifferent magnitudes of pump current vs. lambda (λ) (i.e. the curveshifts). Attempts to compensate for the variations include incorporatinga calibration resistor in the connector to the measuring cell sensor.Unfortunately, this attempted solution does not address all of thevariations. Barometric air pressure and exhaust pressure also influencethe lambda/pump current relationship. Accordingly, the outputs of thesessensors are not accurate. It is therefore desirable to have ameasurement method for oxygen sensors that is self-calibrating andself-compensating for all the above variations.

The pump current vs. lambda curve is also highly temperature dependent.Typical UEGOs contain a heater element that maintains the sensor at thedesired operating temperature. The temperature coefficient of the heaterelement is the quotient of change in resistance (ΔR) to the change intemperature (ΔT). Conventional techniques use the positive temperaturecoefficient of the heater element to regulate input by operating theelement at a constant voltage. Because the temperature coefficient,ΔR/ΔT, is fairly small at the operating temperature, the resultingtemperature regulation is not very precise. Depending on the sensor, thepump cell impedance, the Nernst cell impedance, or both have a muchbigger temperature coefficient, ΔR/ΔT, and would, therefore, allow moreprecise temperature control. It would be more advantageous to controlthe temperature of the pump cell. Unfortunately, at lambda values near1, the pump current is very small or equal to zero and the pump cellimpedance can not be accurately measured on a low current. The Nernstcell is typically physically bonded to the pump cell and, therefore, thetemperature of the Nernst cell and the pump cell differ by a smallamount. In order to measure the Nernst cell impedance, a known fixedcurrent or known fixed voltage have to be impressed on the Nernst celland the resulting voltage or current then measured. Alternatively, asmall alternating current (AC) voltage or current can be impressed onthe Nernst cell and the resulting AC impedance measured. The firstmethod requires stopping the lambda measurement for a period of time andalso requires impressing the reverse charge on the Nernst cell to speedup recovery. The second method does not interfere with the measurementbut requires low pass filters to remove the AC voltage or current fromthe measured signal. The filters also remove the higher signalfrequencies which results in an inability to detect short transientresponses. Both methods measure the temperature of the Nernst cell, notthe pump cell. During operation, a temperature gradient between the pumpcell and the Nernst cell may occur and some temperature control errorsmay result. Therefore there is a need for precise pump cell temperaturecontrol while measuring lambda without resorting to complicatedcircuitry to remove measurement artifacts.

Further, conventional fuel metering techniques result in significantpollution during the warm up period of the oxygen sensor. Inconventional systems where UEGO sensors are used, a precise operatingtemperature must be attained before the UEGO output value is reliable.This increases the time the fuel injection systems runs in ‘open loop’without knowledge of actual air-fuel ratio. As a result, the time theengine creates uncontrolled warm-up pollution is dependent on the sensorwarm-up time. Therefore, there also exists a need for an apparatus,system and method for measuring an oxygen concentration which minimizesthe time before a reliable value is produced by the sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is graphical representation of a relationship between pumpcurrent and an air to fuel ratio, Lambda (λ), for a typical UniversalExhaust Gas Oxygen (UEGO) sensor.

FIG. 2 is a block diagram of the oxygen monitoring device in accordancewith an exemplary embodiment of the invention.

FIG. 3 is a schematic representation of the oxygen monitoring devicewhere the current managing unit is implemented using an analogcomparator circuit and an inverting amplifier circuit in accordance withthe exemplary embodiment of the invention.

FIG. 4 is a flow chart of a method of measuring an oxygen concentrationof a gas in accordance with the exemplary embodiment of the invention.

FIG. 5 is a flow chart of a method of varying the oxygen ion flow withinthe measuring cell in accordance with the exemplary embodiment.

FIG. 6 is a flow chart of a method of calibrating an oxygen measuringdevice in accordance with the exemplary embodiment.

FIG. 7 is a flow chart of a method of determining the oxygenconcentration of a gas by comparing the measured pulse width ratio(PWM_(RATIO)), to the pulse width ratio function in accordance with theexemplary embodiment of the invention.

FIG. 8 is a flow chart of a method of calibrating the heater controlunit in accordance with the exemplary embodiment of the invention.

FIG. 9 is a block diagram of a hand-held diagnostic device suitable forembodying the oxygen measuring device.

DETAILED DESCRIPTION

As explained above, conventional oxygen sensor systems are limited inseveral ways. These limitations are overcome in the exemplary embodimentwhich provides an efficient, low cost, accurate method for measuring anoxygen concentration of gas. An oxygen concentration of a gas ismeasured by varying a pump current through an oxygen measuring cellbased on an output of the measuring cell and observing the pulse widthratio of the resulting square wave representing the pump current.Further, in some circumstances, the method described herein allows thesensor to be used earlier in the warm-up period because the measurementmethod allows the application of a correction factor that compensatesfor the fact that the sensor has not yet achieved its desired operatingtemperature. Also, the exemplary embodiment described herein allowsprecise pump cell temperature control while measuring lambda withoutresorting to complicated circuitry to remove measurement artifacts.

FIG. 2 is a block diagram of the oxygen monitoring device 200 inaccordance with an exemplary embodiment of the invention. The oxygenmonitoring device 200 may be implemented using any combination ofhardware, software and firmware. Various functions and operations of thefunctional blocks described herein may be implemented in any number ofdevices, circuits or elements. Any of the functional blocks may beintegrated in a single device and the functions of the blocks may bedistributed over several devices, circuits and elements.

A measuring cell 202 includes at least a pump cell 204 and an oxygensensor cell 206 where a magnitude and direction of a pump current 208through the pump cell 204 is correlated to a flow of oxygen ions 210within the measuring cell 202. A measuring opening 212 of the measuringcell 202 is positioned to receive a measured gas while an air opening214 faces ambient air. The oxygen sensor cell 206 provides an outputsignal based on the number of oxygen ions within the measuring cell 202.In response to the output signal, a current managing unit 216 varies thepump current between two constant current levels. A first pump currentis maintained by the current managing unit 216 until the output signalreaches a first threshold. When the first threshold is reached, thecurrent managing unit 216 directs the pump current 208 in the oppositedirection until the output signal reaches a second threshold level. Acomputing device 218 monitors the current fluctuation to determine anoxygen concentration of the measured gas. A suitable application of theoxygen monitoring device 200 includes monitoring exhaust gas from acombustion engine to adjust an air-fuel mixture. The oxygen monitoringdevice, method and system may be implemented as part of any of severaltypes of applications and systems. As discussed below, for example, theoxygen monitoring device may be implemented as a hand-held diagnosticdevice, as an original equipment manufacturer (OEM) device within avehicle or as an aftermarket device for permanent installation in avehicle. In addition, the oxygen measuring device 200 may be used tomeasure the oxygen concentration of exhaled gases from a living being todetermine the number of calories that are being expended.

In the exemplary embodiment, the oxygen sensor cell 206 is a Nernst cell(206) that is positioned adjacent to a pump cell 204 in accordance withknown techniques. Other types of oxygen sensor cells 206 may be used,however. It is understood by those skilled in the art that although thefollowing description refers to a Nernst cell (206), the invention maybe implemented with other oxygen sensor cells 206 capable of providingan output signal based on the oxygen level in a measured gas. After acalibration procedure is performed in accordance with the proceduredescribed below, the current managing unit 216 varies the current 208through the pump cell 204 between a constant positive current (Ip) and aconstant negative current (−Ip) based on the output signal of the Nernstcell (206). When a negative current (−Ip) flows through the pump cell204, ambient air is received through the air opening 214 into themeasuring cell 202 through the pump circuit which results in an increaseof the concentration of oxygen within the measuring cell 202. At a highconcentration of oxygen within the measuring cell 202, the Nernst cell(206) provides a low voltage signal output. When an output signal lowerthreshold is reached, the current managing unit 216, directs a positivecurrent (Ip) through the pump cell 204. When a positive current (Ip)flows through the pump cell 204, the oxygen ions in the measuring cell202 flow out to ambient air. Any unburned carbons or fuel within themeasuring cell 202 combine with any remaining oxygen. As a result, themixture of air and unburned carbons within the measuring cell 202decreases in oxygen concentration and increases in fuel concentration.The output signal increases through the transition point where nounburned fuel and no excess oxygen is present in the measuring cell 202.At this transition point, lambda is equal to 1.0 and the Nernst cell(206) provides an output signal of approximately 450 mV. As the positivepump current 208 (Ip) continues to flow, oxygen ions continue to flowout of the air opening 214. As a result, the concentration of oxygencontinues to decrease and the concentration of fuel increases in themeasuring cell 202. The output signal continues to increase until anupper threshold is reached. In response to detecting that the upperthreshold has been reached, the current managing unit 216 changes thedirection of the pump current 208. In the exemplary embodiment, theupper threshold is 455 mV and the lower threshold is 445 mV. Otherthresholds, however, can be used where some suitable values includevalues providing a range that includes the output signal for gas ofambient air and which maintain the Nernst cell (206) within a relativelylinear potion of the lambda to voltage relationship. For example,another suitable pair of values includes 440 mV and 460 mV.

A square wave is formed between the positive and negative currentlevels. The duration of the pump current 208 at positive flow (Ip) andnegative flow (−Ip) depends on the composition of the measured gas.Accordingly, the computing device 218 compares the pulse width ratio(PWM_(RATIO)) of the resulting square wave to a known pulse width ratiofunction to determine the oxygen concentration of the measured gas.

FIG. 3 is a schematic representation of the oxygen monitoring device 200where the current managing unit 216 is implemented using an analogcomparator circuit 304 and an inverting amplifier circuit 306 inaccordance with the exemplary embodiment of the invention. The currentmanaging device 216 may be implemented using any combination andarrangement of hardware, software and firmware. In the exemplaryembodiment, the current managing device 216 includes several hardwarecomponents including resistors, operational amplifiers, analog switches,Zener diodes, logic gates and other circuits. Those skilled in the artwill recognize the various substitutions that can be made for one ormore circuits or circuit elements by applying the teachings herein inaccordance with known techniques. Further, the operating values maydiffer depending on the particular implementation of the currentmanaging device 216.

The inverting amplifier circuit 306 at least includes an operationalamplifier (U₂) 308, an inverting input resistor (R₄) 310, and anon-inverting input resistor (R₅) 312. The voltage at the non-invertinginput of the operational amplifier (U₂) 308 is maintained at voltage ofU_(REF) by a Zener diode 314. U_(REF) is equal to Vcc/2 which isapproximately 2.5 volts in the exemplary embodiment. The pump cell 204in the measuring cell 202 is connected through an analog switch 316between the output of the operational amplifier (U₂) 308 and theinverting input of the operational amplifier (U₂). The operationalamplifier (U₂) 308, inverting input resistor (R₄) 310 and the pump cell204 impedance (R_(pump)) form the inverting amplifier 306 with a gain of−R_(pump)/R₄. The output of the operational amplifier (U₂) 308 isconnected to the analog switch 316 that connects the output of theoperational amplifier 308 to the pump cell 204 in response to the outputlevel of an AND gate (U₃) 318. Since the AND gate 318 provides an active“high” output when the heater control unit 302 presents a “high” enablesignal, the analog switch 316 prevents current from flowing throughmeasuring cell 202 during warm up. Further, as explained below, duringthe calibrate procedure, the analog switch 316 is opened during thenegative pump current 208 cycle resulting in a pump current 208 thatalternates between a positive pump current (IP) and zero.

The inverting input of the operational amplifier (U₂) 308 is connectedto the output of the analog comparator circuit 304 through the invertinginput resistor (R₄) 310. The non-inverting input resistor (R₅) 312, asupply resistor (R₃) 320 and the Zener diode 314 form a voltage dividerand present a reference voltage of (Vcc/2+0.45V) to the inverting inputof an operational amplifier (U₁) 322 of the analog comparator circuit304. In the exemplary embodiment, the reference voltage is 2.95 Voltssince Vcc is 5 Volts. The positive input of the operational amplifier322 is connected to the output of the Nernst cell (206) through asensing resistor (R₁) 324. A feedback resistor (R₂) 326 provides avoltage equal to U_(REF)+0.45V to the positive input of the operationalamplifier 322. Therefore, the operational amplifier (U₁) 322, theresistor (R₁) 324, and the feedback resistor (R₂) 326 form the analogcomparator circuit 304 operating with a hysteresis voltage ofapproximately 10 mV.

The analog comparator circuit 304, the inverting amplifier circuit 306and the measuring cell 202 form an oscillator with a variable pulsewidth modulation (PWM) ratio and a frequency that is dependent on theresponse time of the measuring cell 202. The pump current 208 alternatesbetween +Vcc/(2*R4) and −Vcc/(2*R4). The computing device 218 measuresthe times the output of U2 spends above (t₁) and below Vcc/2 (t2) andfrom that calculates the PWM_(RATIO) and λ according to the functiondescribed below. Lambda (λ) is calculated at every transition of theoutput of the comparator in the exemplary embodiment. The Nernst cell(206) provides an output signal approximately between 0.1 V and 0.7 Vand the resulting (λ) measurement frequency is about 7 octaves higherthan the 3 dB point of the response frequency of the oxygen sensor cell206. Accordingly, the oxygen sensor cell 206 response frequency is wellabove the Nyquist frequency in the exemplary embodiment.

In the exemplary embodiment, the heater control unit 302 increases thetemperature of the measuring cell 202 using a sensor specific method andramp-up schedule. After the measuring cell 202 has achieved itsoperating temperature, the “Ready” output of the heater control unit 302goes active providing a high ENABLE signal to the AND gate (U₃) whichcloses the analog switch 304. The enable signal is also connected to aninput of the computing device 218 and indicates to the computing device218 that the measuring cell 202 is ready for operation. The heatercontrol unit 302 then maintains a constant predetermined voltage overthe heater element or uses other (sensor specific) methods fortemperature regulation. In the exemplary embodiment, the pump cellimpedance is measured when the heater element 330 impedance is at theminimum value. The pump cell impedance is maintained at the measuredvalue by continually monitoring the pump cell impedance and adjustingthe temperature with the heater element 330.

As described below with reference to FIG. 6, the computing device 218stores values in non-volatile memory corresponding to the PWM ratio atthe stoichiometric ratio (PWMST) and the pulse width ratio for air(PWMAIR). In the exemplary method described below with reference toFIGS. 4-8, a nominal lambda value having an error on the order of +/−5%is calculated based on the calibration values and the measured PWMRATIO.Because PWMST is dependent on the characteristics and age of the sensormuch more than on environmental conditions, the calibration process doesnot need to be performed very often in most circumstances.

Based on these teachings, those skilled in the art will recognize thevarious components, devices, and circuits elements that can be used inthe measuring device. An example of suitable device that can be used forthe operational amplifiers 308, 322 include the TLV2463 operationalamplifier available from the Texas Instruments company. Values for theinverting resistor (R₄) 310 and the non-inverting (R₅) resistor 312 areon the order of a few hundred ohms. An example of suitable computingdevice 218 includes an 850 Family RISC 8-Bit Microcontroller. In somecircumstances, some or all of the functional blocks described above maybe implemented as an application specific integrated circuit (ASIC). Forexample, heater control and current managing unit 216 and computingdevice 218 can be easily integrated into a mixed signal ASIC with veryfew external parts.

FIG. 4 is a flow chart of a method of measuring an oxygen concentrationof a gas in accordance with the exemplary embodiment of the invention.The method may be performed with any combination of hardware, softwareor firmware. In the exemplary embodiment, the method is performed in theoxygen measuring device 200.

At step 402, a calibration procedure is performed. The calibrationprocedure obtains the calibration values for initializing the oxygenmeasuring device and may include values related to the characteristicsof the particular measuring cell 202 or related to environmentalconditions. As explained below with reference to FIG. 6, in theexemplary embodiment, values are obtained for maintaining the pump cell204 impedance, for establishing the pulse width ratio function forcalculating lambda, and for adjusting the lambda value when the PWMratio for a stoichiometric ratio (PWM_(ST)) is not zero. Othercalibration values may include parameters related to the frequency of asquare wave of the pump current 208 reflecting oxygen sensorcharacteristics.

At step 404, the oxygen ion flow is varied between a first pump currentand a second pump current based on the output signal of the oxygensensor cell 206. In the exemplary embodiment, the ion flow is varied byalternating the pump current 208 between a positive constant current(IP+) and a negative constant current (IP−). The analog switch 316remains closed during the measurement procedure.

At step 406, the pulse width ratio (PWM_(RATIO)) of the square waveformed by the pump current 208 is determined by the computing device218. In the exemplary embodiment, the pulse widths (t₁ and t₂) of thesquare wave formed by the varying pump current 208 are measured using acrystal clock in the computing device 218. Although individual values ofa single pulse can be measured and stored, the duration of the pulsesresulting form the varying current are averaged over a time period.

At step 408, the pulse width ratio (PWM_(RATIO)) is compared to thepulse width ratio function to determine the oxygen concentration of themeasured gas. In the exemplary embodiment, the computing device 218applies the measured values to equations that utilize the calibratedvalues.

FIG. 5 is a flow chart of a method of varying the oxygen ion flow withinthe measuring cell 202 in accordance with the exemplary embodiment. Theflow chart of FIG. 5, therefore, illustrates an exemplary method ofperforming step 404 of FIG. 4.

At step 502, the pump current 208 is directed in a positive directionthrough the pump cell 204 at a constant magnitude. In the exemplaryoxygen monitoring device 200 described with reference to FIG. 3, theanalog switch 316 remains closed as positive voltage is applied acrossthe pump cell 204. The positive voltage is maintained until the analogcomparator circuit 304 triggers the inverting amplifier 308 to applyinga negative voltage across the pump cell 204.

At step 504, the output signal from the oxygen sensor cell 206 isreceived. In the exemplary oxygen monitoring device 200, the output ofthe oxygen sensor cell 206 is received through the resistor (R₁) 324 atthe positive input of the operational amplifier 322 of the analogcomparator circuit 304.

At step 506, it is determined whether the output signal is greater thanor equal to the upper threshold. If the upper threshold has not beenreached, the method returns to step 502 where the constant positive pumpcurrent is directed through the pump cell 204. If the upper thresholdhas been reached, the method continues at step 508 where the current isreversed and a constant pump current 208 is directed in the negativedirection. As discussed above with reference to FIG. 3, in the exemplaryembodiment, the current managing device 216 includes an analogcomparator circuit 304 and an inverting amplifier circuit 306 to providethe constant current until the thresholds are reached. The analogcomparator circuit 304 triggers the reverse of the pump current 208 inresponse to the detection that the thresholds have been reached.Therefore, the positive pump current (IP+) is maintained until theoutput of the oxygen sensor cell 206 reaches an upper threshold thatcauses the output of the analog comparator circuit 304 to switch to ahigh output changing the output of the inverting amplifier circuit 306.

At step 508, the pump current 208 is directed in a negative direction.In response to the reversed voltage output of the inverting amplifiercircuit 306 the pump current 208 reverses direction and becomes negative(−Ip).

At step 510, the current managing unit 216 receives the output signalfrom the oxygen sensor cell 206. In the exemplary oxygen monitoringdevice 200, the output of the oxygen sensor cell 206 is received throughthe resistor (R₁) 324 at the positive input of the operational amplifier322 of the analog comparator circuit 304.

At step 512, it is determined if the output signal is less than or equalto the lower threshold. Of the lower threshold has not yet been reached,the method returns to step 508 where the current managing unit 218continues to direct the pump current 208 in a negative direction throughthe pump cell 204. Otherwise, the procedure returns to step 502, wherethe current is reversed to the positive direction. Accordingly, in theexemplary embodiment, the current managing device 216 varies the currentbetween 0.445 volts and 455 volts based on the output of the oxygensensor cell 206. As the pump current 208 is varied, characteristics ofthe resulting square wave are measured and stored.

In the exemplary embodiment, the computing device 218 monitors the timeperiods (t₁ and t₂) and if either of the time periods exceeds aoperating threshold, the computing device 218 overwrites the ENABLEsignal and disconnects the pump cell 204 to prevent damage to thesensor. A diagnostic procedure is performed to determine the faultcondition.

FIG. 6 is a flow chart of an exemplary method of calibrating the oxygenmonitoring device 200. The method described with reference to FIG. 6provides and exemplary method of performing the calibration step 402 ofFIG. 4. The oxygen monitoring device 200 may be calibrated in any numberof ways and the particular calibration method used may depend on avariety of factors such as the characteristics of the particular sensor202 and the data that will be collected using the oxygen monitoringdevice 200. In the exemplary embodiment, the calibration procedureincludes calibrating the heater control unit 302 and determining thepulse widths of the varying pump current 208 when the oxygen sensor cell206 is exposed to free air.

At step 602, the oxygen sensor cell 206 is exposed to free air. In theexemplary embodiment, the measuring cell 202 is placed in an area whereexposure to exhaust gases or other air borne impurities is minimized. Insome circumstances where the oxygen measuring device 200 is operating ina functioning vehicle, the computing unit determines that the engine isin a coast down mode when the resulting lambda value is above the leanburn limit for gasoline and not changing over some period of time. Whenit is determined that the vehicle is in a coast down mode, the computingdevice 218 performs the calibration procedure. If the computing device218 is the ECU itself, the coast down condition is already known and theECU, after the predetermined purge time of the exhaust system, performsthe calibration procedure for free air.

At step 604, it is determined whether the heater control unit 302 shouldbe calibrated. In the exemplary embodiment, the heater control unit 302is calibrated during the powering up sequence. Examples of othersuitable situations that require the heater calibration procedure to beperformed include the replacement or reconnection of the measuring cell202 and the detection of certain measurement errors. If heatercalibration is required, the procedure continues at step 606. Otherwise,the proceeds directly to step 608.

At step 606, the heater control unit 302 is calibrated. In the exemplaryembodiment, a preferred heater impedance and a preferred pump cellimpedance corresponding to a preferred operating temperature of theNernst cell 206 are stored in memory. As discussed with reference toFIG. 8, the Nernst cell impedance is maintained at a target Nernst cellimpedance for a suitable time period before the preferred heaterimpedance and the preferred pump cell impedance are measured andrecorded.

At step 608, a sensor warm-up procedure is performed. In the exemplarymonitoring device described with reference to FIG. 3, the analog switch316 is initially opened during the sensor warm-up procedure. Inaccordance with the appropriate heating timetable, power is applied tothe heater element 330 to increase the temperature. The heater controlunit 302 monitors the current and voltage across the heating element 330and determines the impedance of the heater element 330. The heaterimpedance is compared to the preferred heater impedance that wasmeasured and stored during the heater calibration procedure. When theheater control unit detects that the heater impedance is equal to thepreferred heater impedance, the heater control unit 302 determines thatthe minimum operating temperature of the oxygen sensor cell 206 has beenreached. In response to a determination that the desired operatingtemperature is reached, the heater control unit 302 presents a “high”enable signal at the “Ready” output. The AND gate (U3) 318 closes theanalog switch 316 when the ENABLE signal goes “high”.

At step 610, the preferred operating temperature of the Nernst cell ismaintained. The preferred operating temperature is maintained during theremainder of the oxygen sensor calibration procedure as well as duringoperation of the oxygen monitoring device 200. In the exemplaryembodiment, the pump cell 204 impedance R_(PUMP) is constantly monitoredduring operation and the heater control unit 302 is controlled tomaintain a constant, or nearly constant, preferred pump cell impedance.The preferred pump cell impedance is retrieved from memory where it wasstored during the heater calibration procedure. An example of a suitablemethod of controlling the heater control unit 302 includes using pulsewidth modulation to increase or decrease the amount of power dissipatedby the heater element 330.

When the oxygen measuring device 200 is in an oscillating mode and thecurrent is varied, the voltage at the pump cell 204 (output of U₂) isdetermined by Vcc, R_(PUMP), the resistor R₄ 310, and the back-EMF ofthe pump cell 204. The output of the operational amplifier (U₁) 322 ofthe analog comparator circuit 304 switches between 0V and Vcc. Theheater control unit 302 samples the output of the operational amplifier(U₂) 308 before and after each transition of the output of theoperational amplifier (U₁) 322. The absolute value of the differencebetween the voltage measured before and after each transition isU_(DIFF). In some circumstances, the output of the operational amplifier(U₂) 308 is passed through a high pass filter (not shown) ofsufficiently high cut-off frequency. The filter output is sampledimmediately after the transition point and the absolute value ofresulting output voltage is equal to U_(DIFF).

The heater control unit 302 calculates the pump cell 204 impedanceR_(PUMP) in accordance with the following relationship:R _(PUMP) =R ₄(U _(DIFF) /Vcc)  (1)

In some circumstances, the Nernst cell (206) impedance (R_(N)) ismonitored as an alternative or in addition to monitoring the pump cell204 impedance. In order to monitor the Nernst cell (206) impedance, theoutput voltage signal of the Nernst cell (206) is passed through a highpass filter and amplifier (not shown).The resulting filtered andamplified signal is then sampled at the comparator transition point. Thepeak-peak voltage, U_(NPP), is then calculated as the difference betweenthe sample voltage at low-high and high-low transition.

The voltage U_(NPP) follows the equation:U _(NPP) =Vcc(R ₁+2R _(N))/R ₂  (2)

U_(NPP), therefore, linearly follows the Nernst cell (206) impedance,R_(N), and is a convenient measurement for the Nernst cell (206)impedance without the use of any filtering in the signal path toinfluence the measured lambda signal. The resistors, R₁ and R₂, arechosen such that the current through R_(N) is small enough to notinfluence the function of the Nernst cell (206) and such that theU_(NPP) at the Nernst operating temperature and impedance isapproximately 10 mV.

At step 612, the oxygen ion flow 210 is varied between a positivecurrent (Ip) and the negative current (−Ip) based on the output signalof the oxygen sensor cell 206. An example of suitable method of varyingthe current 208 is described above with reference to FIG. 5.

At step 614, the pulse width ratio for air (PWM_(AIR)) is determined. Inthe exemplary embodiment, the pulse widths (t_(1AIR) and t_(2AIR)) aredetermined for the positive current cycle and the negative currentcycle. The transition times of the square wave are timed by a crystalclock within the computing device 218 to measure the pulse widths. Thevalues for the pulse widths are measure and averaged over a sufficienttime period such as one second, for example, to calculate an averagePWM_(AIR).

If the pulse width ratio for air is calculated during a coast downcondition, the computing device 218 determines when the condition isreached before measuring the pulse widths of the pump current 208. Ifthe computing device 218 is an ECU in the system, the ECU detects thecondition based on parameters directly available to the ECU such asthrottle position and engine speed.

At step 616, PWM_(AIR) is stored in memory. Various techniques may beused to store and retrieve calibration information. For example, thepulse widths (t_(1AIR) and t_(2AIR)) may be stored directly into memoryand used for calculating PWM_(AIR) at a later time. Such a procedure maybe desired where the frequency of the square wave is used to furthercompensate for pressure and temperature variations. By storing the pulsewidth timing, frequency information is stored in addition to the averagepulse width ratio for air (PWM_(AIR)).

At step 618, the oxygen ion flow 210 is varied between a first currentand second current based on the output signal of the oxygen sensor cell206. In the exemplary embodiment, the current 208 is varied between (IP)and zero. In a manner similar to the method described above, the current208 is varied from a first current to a second current except that azero current is used in place of the negative current (IP−).

At step 620, the pulse width ratio for air when the second current iszero (PWM′_(AIR)) is determined. In the exemplary embodiment, the pulsewidths (t′_(1AIR) and t′_(2AIR)) are determined for the positive currentcycle and the zero current cycle. The transition times of the squarewave are timed by a crystal clock within the computing device 218 tomeasure the pulse widths. The values for the pulse widths are measureand averaged over a sufficient time period such as one second forexample to calculate an average PWM′_(AIR). To measure PWM_(AIR)′, thecomputing device 218 sets the signal CALIBRATE high. The NAND-Gate (U₄)328 together with AND-Gate (U₃) 318 thus cause the analog switch 316 toswitch on only during the high phase of the pump current 208. During thelow phase, the analog switch 316 is off and no pump current can flow.

At step 622, PWM′_(AIR) is stored in memory. Various techniques may beused to store and retrieve calibration information. For example, thepulse widths (t′_(1AIR) and t′_(2AIR)) may be stored directly intomemory and used for calculating PWM′_(AIR) at a later time.

Other calibration procedures may be performed in some situations.Calibration procedures for pressure and temperature compensation, forexample, may be performed by measuring and storing frequency informationcorresponding to the pump current 208 at certain calibration conditions.

FIG. 7 is a flow chart of a method of determining the oxygenconcentration of a gas by comparing the measured pulse width ratio,PWM_(RATIO), to the pulse width ratio function in accordance with theexemplary embodiment of the invention. The method described withreference to FIG. 7 is an exemplary method of performing step 408 ofFIG. 4.

At step 702, a preliminary oxygen concentration, (λ_(PRE)) iscalculated. In the exemplary embodiment, the preliminary oxygenconcentration (λ_(PRE)) is determined by the following equation:λ_(PRE) =P/(PWM_(AIR)−PWM_(RATIO))  (3)where P=(1+PWM′_(AIR))(1−PWM_(AIR))/(1−PWM′_(AIR))  (4)

The computing device 218 retrieves from memory the values for PWM_(AIR),PWM_(RATIO), and PWM′_(AIR) and applies the above equations to calculatethe preliminary oxygen concentration, λ_(PRE). As explained below, P isequal to PWM_(AIR) where the pulse width ratio at the stoichiometricratio (PWM_(ST)) is zero. Therefore, λ_(PRE) is equal toPWM_(AIR)/(PWM_(AIR)−PWM_(RATIO)) where the PWM_(ST) for the particularsensor is zero.

At step 704, it is determined whether λ_(PRE) is less than one. Ifλ_(PRE) is less than one, the procedure continues at step 706.Otherwise, the procedure continues at step 708, where the oxygenconcentration (λ) of the gas is determined to be equal to thepreliminary oxygen concentration, λ_(PRE).

At step 706, the oxygen concentration (λ) of the gas is determined to beequal to the sum of the preliminary oxygen concentration (λ_(PRE))multiplied by a calibration factor (M) and 1 minus the calibrationfactor (λ=(λ_(PRE))*M+(1−M)). In the exemplary embodiment, a calibrationfactor, M, for the brand and model of the particular measuring cell 202is derived through statistical analysis of the measuring cell's 202performance when exposed to a gas with a known oxygen concentration. Insome circumstances, a calibration factor for each of several measuringcells is stored in memory and applied to the particular model that isconnected within the oxygen measuring device 200. An example of typicalvalue of M is 0.71428.

FIG. 8 is flow chart of an exemplary method of calibrating the heatercontrol unit 302. The method discussed with reference to FIG. 8,therefore, provides an exemplary method for performing step 606 of FIG.6.

At step 802, the heater element 330 impedance is monitored as thetemperature of the heater element 330 is increased. In the exemplarymonitoring device described with reference to FIG. 3, the analog switch316 is initially opened during the heater unit calibration procedure. Inaccordance with the appropriate heating timetable, power is applied tothe heater element 330 to increase the temperature. The heater controlunit 302 monitors the current and voltage across the heating element anddetermines the impedance of the heater element. Based on storedinformation relating the heater element impedance to the temperature ofthe heater element 330, the heater control unit determines when theminimum operating temperature of the oxygen sensor cell 206 is reached.In response to a determination that the desired minimum operatingtemperature is reached, the heater control unit 302 presents a “high”enable signal at the “Ready” output. The AND gate (U3) 318 closes theanalog switch 316 when the ENABLE signal goes “high”.

At step 804 it is determined whether the minimum operating temperaturehas been reached. The procedure proceeds to step 806 when the minimumoperating temperature is reached. Otherwise, the heater temperaturecontinues to be monitored at step 802 with the analog switch 316 opened.

At step 806, the Nernst cell impedance is maintained at the targetNernst cell impedance. The heater control unit 302 is controlled suchthat the temperature is varied to maintain the Nernst cell impedance atthe target value. The target Nernst cell impedance is a predeterminedvalue that depends on the type and brand of the measuring cell (sensor)202 and is provided by the sensor manufacturer. The Nernst cellimpedance is held constant or nearly constant for a minimum time toallow fluctuations in temperatures and impedances to settle. An exampleof a suitable settling time is ten seconds.

As described above, the Nernst cell (206) impedance is monitored bypassing the output voltage signal of the Nernst cell (206) through ahigh pass filter and amplifier (not shown).The resulting filtered andamplified signal is sampled at the comparator transition point. Thepeak-peak voltage, U_(NPP), is calculated as the difference between thesample voltage at low-high and high-low transition in accordance withEquation 2.

At step 808, the preferred heater impedance and the preferred pump cellimpedance are measured and stored. In the exemplary embodiment, the pumpcell impedance is calculated based on Equation 1.As discussed above, thevoltage at the pump cell 204 (output of U₂) is determined by Vcc,R_(PUMP), the resistor R₄, and the back-EMF of the pump cell 204 whenthe oxygen measuring device 200 is in an oscillating mode. The output ofthe operational amplifier (U₁) 322 of the comparator 304 switchesbetween 0V and Vcc. The heater control unit 302 samples the output ofthe operational amplifier (U₂) 308 before and after each transition ofthe output of the operational amplifier (U₁) 322. The absolute value ofthe difference between the voltage measured before and after eachtransition is U_(DIFF). In some circumstances, the output of theoperational amplifier (U₂) 322 is passed through a high pass filter (notshown) of sufficiently high cut-off frequency. The filter output issampled immediately after the transition point and the absolute value ofresulting output voltage is equal to U_(DIFF).

Although various calibration factors and equations may be used dependingon the particular implementation of the oxygen measuring device, theabove equations are derived based on the following analysis andassumptions in the exemplary embodiment. Those skilled in the art willrecognize the modifications based on the teachings herein.

The relationships between the various parameters are described belowwith reference to equations 5-26 where the following is assumed:

Q_(f) is the required oxygen flow in and out of the measuring cell 202to maintain the Nernst cell (206) at the transition point;

Q₁ is an oxygen flow value out of the Nernst cell (206) at the fixedconstant current (Ip);

Q₂ is an oxygen flow value into the Nernst cell (206) at the fixedconstant current (−Ip);

t₁ is the oxygen pump time (Q₁ flow) required to switch the Nernst cell(206) from 0.445V to 0.455V; and

t₂ is the oxygen pump time (Q₂ flow) required to switch the Nernst cell(206) from 0.455V to 0.445V.

For the forgoing assumptions, therefore, the Nernst cell (206) voltageis 0.45V with an alternating current (AC) component of 10 mVpp. Theresulting Q_(f) is:Q _(f)=(Q ₁ *t ₁ −Q ₂ *t ₂)/(t ₁ +t ₂)  (5)

The timing relationships can be expressed asPWM_(RATIO)=(t ₁ −t ₂)/(t ₁ +t ₂)  (6)

Using 1 and 2,equation 1 can be rewritten as:Q _(f)=[(Q ₁ +Q ₂)*PWM_(RATIO) +Q ₁ −Q ₂)]/2  (7)

Pump flow ratio (Q_(RAT)) can be expressed as:Q _(RAT)=(Q ₁ −Q ₂)/(Q ₁ +Q ₂)  (8)

At changing air pressure, Q₁ and Q₂ change approximately proportionallyand, therefore, Q_(RAT) stays nearly constant. The same holds true fortemperature changes. Accordingly, Q_(RAT) is independent of temperature.

In some circumstances, Q_(RAT) may change when the sensor ages and,therefore, the sensor may need to be periodically calibrated to maintainoptimal performance.

If Q₁ and Q₂ are known and are constants, the oxygen flow rate andLambda, (λ) is determined from the timing relationship, PWM_(RATIO),which is measured. Q₁ and Q₂ are constant if the pump current 208,temperature, exhaust pressure, barometric pressure and oxygenconcentration in air are constant. In the exemplary embodiment, the pumpcurrent 208 and temperature are held constant through careful circuitdesign. For the analysis described herein, the atmospheric oxygenconcentration is assumed to be constant at 20.9%. Barometric pressureeffects are compensated through calibration. The effect of exhaustpressure tends to modify both, Q₁ and Q₂ by an equal factor and alsomodifies the response time of the oxygen sensor cell 206 because more orless oxygen ions are present at the oxygen sensor cell 206 surfacedepending on pressure.

As described above, the oxygen monitoring device 200 measures oxygenflow by switching the pump current 208 between a constant positive andnegative value. The absolute value for this constant pump current valueis chosen such that it is greater than the absolute value of the pumpcurrent 208 required for free air.

The above equation is linear and can be determined with two knownpoints. The time values t₁ and t₂ are measured by a crystal controlledmicroprocessor or timer circuit which allows the accurate determinationof Lambda, (λ), once the two calibration points are known.

A stoichiometric exhaust mixture does not require any corrective oxygenflow and the steady state pump current 208 is, therefore, equal to zero.This condition is used to determine one of the calibration points, thestoichiometric pulse width ratio, PWM_(ST).

As described above, a second calibration point is obtained by measuringthe pulse width ratio when the measured gas is air. The measuring cell202 is exposed to free air. If the measuring cell 202 is not installedin a vehicle, the measuring cell is placed in an area exposed to freeair. If the measuring cell 202 is installed in a vehicle, thecalibration for free air is performed when the vehicle has not been inoperation for an adequate time and all the exhaust gases have dissipatedor when the vehicle is in a cost-down mode. During the coast-down mode,the throttle on the engine is completely closed and engine speed isabove a predetermined value. In this case, a typical ECU will not injectany fuel because no power output is required from the engine and furtherfuel can be saved. The pump cell 204 is then driven with a total flowvalue Q_(F) that is high enough to pump all oxygen from the air in themeasurement chamber.

From equations 5 through 8 follows:PWM_(ST) =−Q _(RAT)  (9)

The lambda value, λ, calculated from exhaust oxygen concentration can beexpressed as:λ=Air Oxygen content/(Air Oxygen content−Excess Oxygen)  (10)

Note that the value Excess Oxygen in Equation 6 can have negative valuesif all oxygen is consumed but unburned or partially burned fuel is stillpresent.

To examine the oxygen flow rate instead of volume, t is eliminated bydivision:λ=Q _(f(AIR))/(Q _(f(AIR)) −Q _(f)):  (11)

applying equations 7,8,9,and 11:λ=(PWM_(AIR)−PWM_(ST))/(PWM _(AIR) −PWM _(RATIO))  (12)

As described above, a second free air PWM ratio (PWM′_(AIR)) is measuredby switching the pump cell 204 between Q₁ and no current (Q₂=0) duringfree air calibration.

PWM_(ST) is calculated during calibration from PWM_(AIR) and PWM′_(AIR)according to the following formulas:

From equation 7,2*Q _(f)=(Q ₁ +Q ₂)*PWM_(AIR) +Q ₁ −Q ₂  (13)2*Q _(f) =Q _(1*PWM′) _(AIR) +Q ₁  (14)

Where PWM′_(AIR) is measured when switching between Q₁ and no currentinstead of Q₁ and Q₂.P=PWM_(AIR)−PWM_(ST).  (15)

From equations 13 and 14:P=(1+PWM′_(AIR))*(1−PWM_(AIR))/(1−PWM′_(AIR))  (16)PWM_(ST)=PWM_(AIR) −P  (17)

Applying equation (12):λ=P/(PWM_(AIR)−PWM_(RATIO))  (18)

As explained above, PWM_(AIR) is measured by exposing the sensor to freeair at the appropriate operating temperature and, in some circumstances,frequency information is used for determining compensation factors. Thefollowing analysis demonstrates the relationship between frequency andother parameters.

Returning to equation 8,if Q₁=Q₂, Q_(RAT) (and therefore PWM_(ST))becomes zero. The actual sampling frequency is dependent on the fullflow ratio, Q_(F).

Equation 8 then changes to:Q _(f) =Q _(F)*PWM_(RATIO).  (19)

Equation 12 becomesλ=PWM_(AIR)/(PWM_(AIR)−PWM_(RATIO))  (20)

Q_(F) is a function of the pump current 208, Ip, and, therefore,Q_(F)=f(Ip). If Q_(F) for a constant Ip changes because of exhaustpressure changes, the measured PWM_(RATIO) becomes PWM′_(RATIO) for thesame corrective flow, Q_(f).

With exhaust gas pressure or temperature changes Q₁ and Q₂ change by afactor K in a first approximation.

Equation 8 then becomes:Q _(f) =K*[(Q ₁ +Q ₂)*PWM′_(AIR) +Q ₁ −Q ₂)]/2  (21)

whereQ ₁ *t ₁ =K*Q ₁ *t ₁′  (22)Q ₂ *t ₂ =K*Q ₂ *t ₂′  (23)

The measurement frequency f is determined by:f=1/(t ₁ +t ₂)  (24)f′=1/(t ₁ ′+t ₂′)  (25)

From equations 20, 21, 22 and 23 follows:K=f′/f  (26)

Because f is constant when all other environmental conditions areconstant, this calculation can be used to correct for temperature and/orpressure changes. Equation 8 then becomes:λ=(PWM_(AIR)−PWM_(ST))/(PWM_(AIR)−(1−K)*PWM_(ST)−K*PWM_(RATIO))  (27)

and equation 18 becomes:λ=PWM_(AIR)/(PWM_(AIR)−K*PWM′_(RATIO))  (28)

These equations, therefore, allow the application of a pressurecompensation factor, K to compensate for pressure or temperaturechanges. Under extreme circumstances, Q₁ and Q₂ do not change equally bythe same factor K. In some situations, therefore, the normalizedfrequency deviation f′/f is used as an index into an experimentallyderived lookup table to extract the accurate deviation factor K′:K′=func (f′/f).  (29)

The calculated Lambda value can thus be corrected for exhaust pressurechanges without the use of separate sensors to measure exhaust pressureonce a normalized frequency/lambda table is experimentally determinedfor a given sensor type.

Conventional commercially available packaged measuring cells 202 oftenhave temperature dependent parasitic resistances to the virtual groundof the pump cell 204 and Nernst cell (206). This parasitic resistancemust be addressed through software or circuitry in order to applypressure compensation methods described above with many commerciallyavailable measuring cells 202.

The forgoing equations and analysis may be applied to otherimplementations of the invention in ways other than described above andthe teachings described herein may be applied to a variety of formats,implementations and configurations. As explained above, the hardware andsoftware may be modified to accommodate a variety of factors. Forexample, the analog switch 316 can be eliminated where the operationalamplifier (U₂) 308 provides a tri-state output. Also, the analog switch316 can be connected within the oxygen measuring device 200 before theinverting resistor (R₄) 310 instead of connecting to the output of theoperational amplifier (U₂) 308. The operational amplifier (U₂) 308 mayalso provide a tri-state output. In addition, the heater controllingunit 302 may be integrated as part of the computing device 218.

Further, the Zener diode 314 may be replaced with a digital to analog(D/A) converter or a potentiometer in some circumstances. The referencesvoltage U_(REF) could thereby be set such that the pulse width ratio atthe stoichiometric ratio, PWM_(ST) is exactly zero. In such acircumstance, the equation used to calculate λ is:λ=PWM_(AIR)/(PWM_(AIR) −K*PWM′)  (30)

In some circumstances, frequency information is analyzed to provideother useful information or data in accordance with the analysis above.For example, because the response time of a measuring cell 202 changeswith aging, the oscillating frequency is used directly as a measurementto determine the need for replacement. When a lower threshold frequencyis reached, the computing device 218 may provide a warning that thesensor should be replaced. The frequency analysis is preferablyperformed when the free-air value is recalibrated because theenvironmental conditions are comparable (f′ and f in equation 27 areequal) and the frequency change is due to aging of the sensor.

FIG. 9 is a block diagram of an exemplary hand-held diagnostic devicesuitable for embodying the oxygen measuring device 200. As mentionedabove, the oxygen measuring device 200 may be implemented as any ofseveral configuration and devices. The oxygen measuring device 200, forexample, may be integrated as an OEM device in a vehicle fuel system.Further, the oxygen measuring device 200 may be part of an in-vehicleaftermarket fueling system or diagnostic system. Other devices and useswill be readily apparent to those skilled in the art based on theteachings herein.

The exemplary hand-held diagnostic device 900 includes a housing 902, adisplay 904, connectors 906-912, and buttons (or other type of switches)912, 914 that provide interfaces to the computing device 218 and thecurrent managing device 216. The display allows the user to viewinformation regarding the status to the hand-held diagnostic device 900.In the exemplary hand held device 900, the connectors 906-912 include aserial port 912 for connecting to an external computer, analog outputconnector 908 for supplying an analog signal corresponding to themeasured λ, an auxiliary sensor interface 919, and a sensor connector906. Other connectors such as a power connector for receiving DC supplypower, for example, are also included in some circumstances. A calibratebutton 908 connected to the computing device 218 provides a userinterface for initiating the calibration procedure. A record button 914provides a user interface for initiating a record procedure that allowsseveral seconds of data to be stored in memory. An example of anotherbutton or switch that may be used includes an on-off switch (not shown).The buttons and connectors are connected to the computing device 218 andother circuitry and provide interfaces between the user, the measuringdevice 200, the measuring cell 202 and other external equipment.

Therefore, the system, apparatus and method for measuring the oxygenconcentration of gas provides a cost effective, efficient and accurateway to monitor a gas having several advantages over conventionalsystems. The techniques described herein provide a simplified designsince no analog to digital (A/D) conversion is required for a oxygenconcentration (λ) measurement. Further, no calibration resistor isrequired in the measuring cell sensor to compensate for sensortolerances which results in simplified production and lower productioncosts. Wide tolerances of the measuring cell 202 itself are acceptable,resulting in higher possible production yield. Because no precisionresistors or other precision parts are required, circuit cost isminimized. The oxygen monitoring device 200 self-compensates forpressure and temperature variations. The measurement process isconverted to the time-domain, instead of an analog current/voltagedomain. By using standard crystal time bases, as is typical in digitaldesigns, temperature and age-related drifts are eliminated becausecrystal time bases have tolerances of <10⁻⁶ compared to <10⁻² fortypical resistors. Measurement results are linear to 1/Lambda andindependent of the Ip/Lambda curve of the sensor. Calibration isconvenient and uses only air as a reference gas.

Clearly, other embodiments and modifications of this invention willoccur readily to those of ordinary skill in the art in view of theseteachings. Therefore, this invention is to be limited only by followingclaims, which include all such embodiments, equivalents, andmodifications when viewed in conjunction with the above specificationand accompanying drawings.

1. A method of measuring an oxygen concentration of a gas, the methodcomprising: receiving an output signal from an oxygen sensor cellpositioned within a measuring chamber; varying a flow of oxygen ionswithin the measuring chamber by varying a pump current through a pumpcell controlling the flow of oxygen ions between a first constant pumpcurrent and a second constant pump current in response to the outputsignal; and determining the oxygen concentration of the gas based on thepump current.
 2. A method in accordance with claim 1, wherein thedetermining comprises: determining the oxygen concentration of the gasby comparing a pulse width ratio of a resulting square wave of the pumpcurrent to a pulse width ratio function.
 3. A method in accordance withclaim 2, wherein varying the flow comprises: directing the pump currentin a positive direction at a constant magnitude until the output signalreaches an upper threshold; and directing the pump current in a negativedirection at the constant magnitude until the output signal reaches alower threshold.
 4. A method in accordance with claim 3, whereindirecting the pump current in a positive direction and directing thecurrent in a negative direction forms an oscillating output signalhaving a varying pulse width ratio and a varying frequency.
 5. A methodin accordance with claim 4, further comprising: compensating for anoffset of the oxygen concentration based on environmental conditions. 6.A method in accordance with claim 5, wherein the compensating comprisesadjusting a value for the oxygen concentration of the gas based on thefrequency of the oscillating output signal.
 7. A method in accordancewith claim 5 wherein the compensating comprises changing a temperatureof the pump cell based on the frequency.
 8. A method in accordance withclaim 6, wherein adjusting the value for the oxygen concentration of thegas comprises: determining an operating pump cell impedance of the pumpcell; and applying a corresponding Lambda associated with the operatingpump cell impedance.
 9. A method in accordance with claim 8, wherein thecompensating comprises changing a temperature of the pump cell based onthe frequency.
 10. A method in accordance with claim 8, whereindetermining the operating pump cell impedance comprises: determining again of an inverting amplifier circuit directing the current, theinverting amplifier comprising an operational amplifier having an outputconnected to the pump cell, and an input resistor connected to the inputof the operational amplifier.
 11. A method in accordance with claim 2,further comprising: performing a calibration procedure by determining atleast some factors of the pulse width ratio function.
 12. A method inaccordance with claim 11, wherein performing the calibration procedurecomprises: exposing the oxygen sensor cell to a known gas with a knownoxygen concentration; and determining a corresponding oxygen ion flowfor the pump current.
 13. A method in accordance with claim 12, whereindetermining the corresponding oxygen ion flow for the pump currentcomprises: determining a relationship between a Lambda coefficient ofthe oxygen sensor cell and the pulse width ratio.
 14. A method inaccordance with claim 13, wherein determining a relationship between theLambda coefficient of the oxygen sensor cell and the pulse width ratiocomprises: determining at least two points on a line representing therelationship between Lambda and the pulse width ratio.
 15. A method inaccordance with claim 14, wherein determining at least two points on theline representing the relationship between Lambda and the pulse widthratio comprises: directing the pump current in the positive directionuntil the upper threshold is reached; directing no pump current until alower threshold is reached; and observing a calibration pulse widthratio.
 16. A method in accordance with claim 11, wherein performing thecalibration procedure comprises: exposing the oxygen sensor cell to afirst known gas with a known oxygen concentration; determining apositive corresponding oxygen ion flow for a positive constant pumpcurrent; and determining a negative corresponding oxygen ion flow for anegative constant pump current.
 17. A method in accordance with claim 1,wherein varying a flow of oxygen ions within the measuring chambercomprises: applying an input voltage at a resistor connected to anegative input of an inverting amplifier to vary the pump currentthrough the pump cell in response to the output signal.
 18. A method inaccordance with claim 17, further comprising: determining the oxygenconcentration based on the input voltage.
 19. A method in accordancewith claim 18, wherein determining the oxygen concentration comprises:applying a pulse width ratio of a square wave representing the pumpcurrent to a pulse width ratio function.
 20. A method in accordance withclaim 19, wherein determining the oxygen concentration furthercomprises: measuring a first time period of a positive pulse of thesquare wave corresponding to the first constant pump current; measuringa second time period of a negative pulse of the square wavecorresponding to the second constant pump current; and calculating thepulse width ratio by dividing the difference between the first timeperiod and the second time period by the sum of the first time periodand the second time period.
 21. A method in accordance with claim 20,wherein applying the pulse width ratio comprises calculating the oxygenconcentration in accordance with the equation:λ_(PRE)=P/(PWM_(AIR)−PWM_(RATIO)), whereP=(1+PWM′_(AIR))(1−PWM_(AIR))/(1−PWM′_(AIR)), λ_(PRE) is the oxygenconcentration, PWM_(RATIO) is the pulse width ratio, PWM_(AIR) is apulse width ratio for free air when the second current is negative, andPWM′_(AIR) is a pulse width ratio for free air when the second currentis zero.
 22. A method in accordance with claim 21, wherein applying thepulse width ratio further comprises calculating the oxygen concentrationin accordance with the equation λ=M*λ_(PRE)+(1−M), where λ is the oxygenconcentration when λ_(PRE) is less than one, and M is a constantrepresenting a correction factor for the measuring cell.